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5.62 of an unknown gas at STP require 52.25J of heat to raise the temprature by 10°c at constt vol. Find Cp,Cv and atomicity of gas.
Answers
Explanation:
At STP a gas of 22.4 \: dm^322.4dm3 will be equivalent to " 1 mole".
Therefore for 5.6 \: dm^35.6dm3 of the gas at STP will be equivalent to :
= > \begin{gathered}\bf{\frac{1}{22.4} \times 5.6} \\\end{gathered}22.41×5.6
= > \begin{gathered}\bf{0.25 \: moles} \\\end{gathered}0.25moles
As mentioned in the query there is a temperature rise of "10°C", for the value of "0?25 moles" of the gas at a constant volume of 10°C the required heat would be (given) = 52.25 Joules.
Therefore for a rise of temperature in about "1°C", 1 mole of that gas in a constant volume will've the heat requirement of :
= > \begin{gathered}\bf{\frac{52.25}{10 \times 0.25} \: Joules} \\\end{gathered}10×0.2552.25Joules
= >\begin{gathered}\bf{\frac{52.25}{2.5} \: Joules} \\\end{gathered}2.552.25Joules
= > \bf{20.9 \: Joules}20.9Joules
\begin{gathered}\boxed{\bf{\therefore \: \: C_v = 20.9 \: Joule \: Kelvin^{- 1} \: mole^{- 1}}} \\\end{gathered}∴Cv=20.9JouleKelvin−1mole−1
Therefore, to calculate \bf{C_p}Cp .
\bf{C_p = C_v + R}Cp=Cv+R
\begin{gathered}\bf{\therefore \: \: C_p = 20.9 \: Joule \: Kelvin^{- 1} \: Mole^{- 1} + 8.314 \: Joule \: Kelvin^{- 1} \: Mole^{- 1}} \\\end{gathered}∴Cp=20.9JouleKelvin−1Mole−1+8.314JouleKelvin−1Mole−1
\begin{gathered}\boxed{\bf{\therefore \: \: C_p = 29.214 \: Joule \: Kelvin^{- 1} \: Mole^{- 1}}} \\\end{gathered}∴Cp=29.214JouleKelvin−1Mole−1
Now, for calculating the unknown gas's atomicity or to check whether it's monoatomic, diatomic etc.
\begin{gathered}\bf{\therefore \: \: \gamma = \frac{C_p}{C_v}} \\\end{gathered}∴γ=CvCp
\begin{gathered}\bf{\therefore \: \: \gamma = \frac{29.214}{20.9}} \\\end{gathered}∴γ=20.929.214
\begin{gathered}\boxed{\bf{\therefore \: \: \gamma = 1.4}} \\\end{gathered}∴γ=1.4
Therefore the given unknown gas's atomicity is \boxed{\bf{Diatomic \: Gas}}DiatomicGas .